Essays on Algebra

Application of Algebra in computing

Algebraic principles are used extensively in computing. In computer science, the computer algebra is called algebraic computation or symbolic computation. This is used mainly in software development and the associated algorithms that are used in the manipulation of mathematical expressions and objects. Kaltofen Erich (1982) noted that the long-known algorithms that were being used proved to be very long and this necessitated the revisiting of classical algebra with the intention of making them effective and efficient. In specific terms, algebra is used in the following fields of computing.
Encoding: in encoding, data that is arranged in arrays or matrices Continue reading...

Before the onset of the seventeenth century, the Middle East had dominated in the area of mathematical ideas. Many philosophers and scientists came up with compelling ideas in mathematics and proved many formulas in mathematics from the Middle East. Essentially, there were distinct factors that influenced scholars and philosophers from this region to be competent in mathematics and other scientific inventions as they were. However, in the onset of the seventeenth century, Europe replaced the Middle East, which had been vastly associated with mathematical discoveries. Europe thus became the new engine house of mathematical ideas from the seventeenth century . Continue reading...

Instructional leader

Abstract
This essay will discuss tools, which will assist the educational leader in promoting the learning outcome and assessment of students by guiding, encouraging, motivating and supporting the school culture and offering instructional programs in the area of mathematics, which are conducive to student learning and the professional growth of staff members. Mathematical tools are measured and structured to assist teachers who can examine distinct or various approaches to improve the mathematics performance of students in middle school. Students that are in elementary grades 3 through 9 accept the challenge and the desire to succeed. According to research, students Continue reading...

CRITIQUE OF “THE ALGEBRA OF INFINITE JUSTICE”

The Algebra of infinite justice is an article written by Arundhati Roy. Arundhati was born on Novemeber 24, 1961 in Shillong to a Bengali Hindu father and a Christian mother. She won a Booker Prize for her first novel-The God of Small Things in 1997. After that she wrote on many topics on politics, nuclear weapons s in India, corruption among others. One of her writing is “The algebra of infinite justice” where she criticizes the role of USA in the beginning, propagation, and methods to fight terrorist. She claims the USA is created terrorist and is attempting to Continue reading...

Principal concept analysis may be defined as the statistical analysis tool relevant for the transformation of detailed or complex data into simple and easy to understand data. The method focuses on the use of principal components of statistics for possible interpretations. In most cases, the method does not include statistical assumptions. However, the method will always give extremely significant results for data that contains multivariate normal distribution. The data is extensively significant in determining the hypothetical variables or components that are extensively useful in the multidimensional data. In other words, the method PCA is a method significant in projecting Continue reading...

Mid-Term

Cope
Bloom’s Taxonomy in Mathematics Teaching
Bloom’s and Anderson’s Taxonomy
This paper discusses a brief history and background of the original Bloom’s taxonomy established in 1956 and the revised Bloom’s taxonomy by Anderson et al. in 2002. It attempts to explore how the taxonomy of learning in the cognitive domain is applied in a specific teaching field such as Mathematics.
In 1956, Benjamin Bloom headed a committee of educators to establish a systematic hierarchy in classifying educational objectives. They published their findings in a book, Taxonomy of Educational Objectives: The Classification of Educational Goals ( Continue reading...

The Binary System is the simplest numeration of all positional number systems. The basic of this system is discovered by Gottfried Leibniz, who was also the co-creator of Calculus, in his work Explication de l'arithmétique binaire in 1679. In this work, he was trying to translate verbal statements into mathematical ones.
Yi Jing, which was said to be created by the so-called Third millennium father of Chinese writing Fu Xi, depicts yin and yang. It was represented in binary, with yin as 0 and yang as 1, involving eight trigrams and sixty-four hexagrams. Leibniz’s works were ignored Continue reading...

Education is by far the most important activity in a person’s lifetime. It is said that education never ends and a person’s capacity to learn is only limited to his or her belief of the knowledge they possess. Educational institutions all over the world impart knowledge to young minds in various fields established by human kind throughout its existence. However, education is not only about gaining knowledge and certifying oneself (Hacker). It is about increasing one’s awareness, one’s own personality and one’s one perspective of the world around them. However, each individual has a Continue reading...

Introduction to Electrical Engineering

Electronic gadgets are in great demands today because of the evolution of high technology and advancement of internet connection. People are always finding something new, so, many companies are giving funds for research. With the help of electrical engineers, companies are providing new gadgets every now and then to surpass the features of the previous gadgets that they have been produced.
In order for the students to solve complexities of a problem, electrical engineering program gives an opportunity to learn new things by experimentation and analytic solving. Therefore, this program mainly tackles mathematics and science. Because of experimentation and Continue reading...

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Wolfram Alpha is modern powerful search engines that caters various fields of studies launched in May 2009. The design of these engines initially concentrates on formula and algorithm growth in Mathematics as a result of extensive and sustained data gathering conducted by the team .
In the field of mathematics, it provides supports on specific categories of topics such as mathematical functions, algebra, computational sciences, probability and statistics, calculus and analysis, geometry as well as discrete mathematics. Beyond the common mathematical functions, the team of Wolfram recently added Bessel functions, zeta functions, gamma Continue reading...

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Introduction
Euclid (near 365 - 300 BC) is a Greek mathematician, lived in Alexandria, in the 3rd BC. The main work "Elements" (15 books), containing the basics of ancient mathematics, elementary geometry, number theory, the general theory of relations and the method of determining areas and volumes, which included elements of the theory of limits, has had an enormous influence on the development of mathematics. He worked on astronomy, optics, music theory.
Information about the time and place of his birth did not reach us, but we know that Euclid lived Continue reading...

There are several mathematical formulae that mathematicians and scientists have come up with over time. These mathematics formulae solve or address several issues or problems in the real world or mathematical and scientific field. One of the well-known mathematicians is Augustin Louis Cauchy. He is credited for coming up with the Cauchy sequence (the Cauchy sequence is named after him). This paper explores the Cauchy sequence, explaining its nature, form, application, and other related aspects of the sequence.
What is Cauchy sequence? This is a sequence whose elements become arbitrarily close to each other in the course of progression Continue reading...

The fundamental theorem of algebra (FToA) is states that each non-constant single-variable polynomial with complex coefficients has at least one complex root. In fact, there are many equivalent formulations, such as this: every real polynomial can be represented as a product of real linear and real quadratic factors.
Early studies equations by al-Khwarizmi (from 800) are devoted only to positive real roots and have no relation to the FToA. Cardano was the first to realize that it is possible to work with the values ​​more general than real numbers (Geuvers, Wiedijk & Zwanenburg, 2002). This discovery was made in the Continue reading...

Solving Real-World Problems Using Algebra.

A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P= -25x2+300x . What number of clerks will maximize the profit, and what is the maximum possible profit?

Solution

The Quadratic equation P= -25x2+300x can be modified to the form y= -25x2+300x, where P= y.
Modifying the equation in this form enables us to plot the function y= -25x2+300x

For various values of x where x is a positive integer.

The general equation of a quadratic is given by y= ax2+bx+c where a, b and c Continue reading...

The article, “Predicting Human Brain Activity Associated with the Meanings of Nouns” was written by Tom M. Mitchel, Svetlana V. Shinkareva and their five associates. The article was published in Science in May 2008. It outlined a computational program that predicted which parts of the brain were stimulated and would respond to certain words and images, or certain stimuli. I found several concepts of the article very interesting. For example, the basis of the article’s studies was founded on creating a computational framework subject to linguistics. In layman terms, a grid of the mind was drawn up, based Continue reading...

Aims

The main aim of the experiment was to verify the vector cross product and its torque.
Other aims were to understand the mathematical model of carrying out the vector cross product and to determine the equilibrium in a system under torque.

Introduction

In the manipulation of vectors through multiplication two kind of products are achieved, the dot product and the cross product. The dot product of a vector is a scalar quantity and hence it only has magnitude. An example of scalar quantity is work done by a force.
The cross product of a vector produces a quantity that has Continue reading...

200 Years of Eastern and Western Medicine and Science

200 Years of Eastern and Western Medicine and Science – Comparison of Developments between 1800-1900
1 Introduction
Thesis Statement: The period between 1800-1900 marked the evolution of Eastern and Western science and a significant cultural exchange that laid the foundation of modern day globalized science.
The purpose of this paper is to trace the development of science and medicine across two centuries in both the East and the West. The timeframe that has been selected for the study extends across the 19th to the 20th century which is a very important Continue reading...

Validity and Scope of Approximate Methods of Integration

Introduction
Addition of discrete numbers is pretty straightforward; more than 80% of the human population can make mental calculations instantly. So when integration was introduced as a kind of addition in a continuous domain, I was not very worried. However, it didn’t take me long to realize that understanding integration is more than solving a bunch of problems using well defined techniques. So in my pursuit to understand the topic well, I decided to research upon how some of these techniques (Trapezium Rule and Simpson’s Rule) came about, how they work, and what they really mean. With Continue reading...

QUESTION 1

Function – A function is the relationship that exists between an input and output such that one input has only one possible output. This implies that a function takes an input and produces an output based on the input (Cheney & Kincaid, 2012).

Examples

Linear function
y = 2 x

Quadratic function

y = 2 x2

Third degree polynomial

y = 2 x3

Exponential function

y = e2x

Logarithmic function

y = log 2 x

Periodic function

y = sin x
Domain of a function - The domain of a function is the set of inputs for which the output of the function exists (Cheney & Kincaid, 2012).The domain of linear function is (- ∞ to ∞), quadratic function is (- ∞ Continue reading...

Kirchhoff’s Laws are fundamental in the analysis of electrical and electronic circuits. They describe the behavior of linear circuits accurately, and work well with approximations in other types of systems as well, making them extremely useful (“Electrical Principles”, 2013). Further, they are more popular and widely used than Maxwell’s equations, from which they can be derived. This is because Maxwell’s equations are very complex and involve brute Mathematics to solve even simple circuits, while the Kirchhoff’s laws are relatively much easier to use in most cases.

There are two laws which were given by Kirchhoff:

1) Kirchhoff’s Current law (KCL)
2) Kirchhoff’s Continue reading...

Given Traffic Scenario

Figure 1: The intersections of five one-way streets
1) There are five streets making six intersections. All the streets are one-way, that is, cars can move along only one direction on any street. The number of cars between intersections is the taken to be the traffic flows. For optimal flows, it is assumed that the number of cars entering an intersection in a given time must equal the number of cars leaving that intersection in that time. Also the number of cars entering and leaving any street per unit time is as mentioned in Figure 1. It is important Continue reading...

The properties of real numbers is a fundamental concept of basic algebra. Any given individual should be aware of these concepts as we may face them in our everyday lives without even noticing. When you actually are doing simple math operations while buying groceries or calculating your monthly expenses, you are dealing with real numbers, and, therefore, you should be aware of their properties in order not to make a mistake in your calculations. The distributive law, simplification procedures and operations with removing parentheses are important to know anytime you are facing a problem which involves calculations. The knowledge Continue reading...

“An educated Petersburg, is a successful Petersburg”

Introduction
Petersburg is an independent American city found in the Virginia state of the United States. Its population is overwhelmingly black with an estimated percentage of 79. The city has got a rich industrial history and once supported a booming tobacco industry. Petersburg boasts of several schools in all learning levels.

Overview of the campaign

Generally, Petersburg education standards are adversely reviewed in all quarters. This is a view well rooted in the collective mind of the nation. Recently, a study was conducted on the relationship of education standards and affluence. It was noted that poorer kids do worse than their richer counterparts. Continue reading...

Mathematics and sciences gave me one of the biggest challenges in my early education life. Having studied in a private school in the US where I was introduced to Everyday Math, I realized that it was not as easy as the tutors would want us to believe. An s early as I can remember, the educators used old and ineffective teaching criteria. Having to count from 0 to 1000 and playing games seemed tedious at the moment but it was as much impractical as I would learn later on. Addition and subtraction facts were scanty, and less emphasized. Until Continue reading...

A.1A single mom has to go back to work and needs day care for her baby. She is trying to decide between a baby sitter, who cares for children in her home,ora nearby day care center. The baby sitter charges a flat rate of $10 per hour, and the localday carecenter charges $325 per week, for 5 days per week, up to 40 hours. (Mon-Fri), plus $10 per hour for any time exceeding 40 hours.
A.2The baby’s mom will need day care services M-F from 7:30-5:30 (10 hours per day, or 50 hours per week).
A.3The baby Continue reading...

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Part 1. Data collection.

Gather from credible sources the following data:

- The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli
- The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn
- The recommended daily values (in milligrams) of calcium and iron
We have found that in 10 oz broccoli there are 116.44 mg of calcium and 2.04 mg of iron.
Also we found, that in 1 cup of frozen corn there are 3.28 mg of Continue reading...

Before the age of Mohammed Muslims said that their people lived in the age of ignorance and the Arabian Peninsula was an archaic place that housed a myriad of religions and cultures – some sort of political wasteland (Basif, 2013). The Bedouins were the nomads that occupied the peninsula and provided the backbone for the social atmosphere. They were skilled travellers and controlled the commercial networks. While the peninsula housed a lot of towns and cities, Mecca stood out from them all. It was not a major trading city or a crossroad to one but it stood near an oasis Continue reading...

Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".

Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems.
As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of ( Continue reading...

This is a report paper which provides a brief summary of introduction to linear algebra by John R. Durbin. The paper shall provide a brief summary of the three chapters of the book; chapter 11, 12 and thirteen.

Introduction

Modern algebra has been causing much difficulty to the learners and the professors as well. This is attributed to the complexity of the unit and elaborative theorems and formula used in the unit .therefore in this papers I have tried to simplify the theorems and formulas to easen the understanding of the topics such as Galois theorems permutation and many more. Continue reading...

Corse title:

1.
Using Boolean algebra laws, a negation is denoted by a NOT gate in the circuit. Assume the input signal at X is 1. As it passes the NOT gate it becomes 0. Using Boolean algebra, note that NOT gate is a negation of the input signal, which is 1, hence the output becomes 0. This 0 is the input of the OR gate. This similar to the Y but, at Z the signal is not affected since there is no negation by NOT gate. The truth table for OR is a mathematical representation of Boolean algebra on logics Continue reading...

Introduction

Islam also has a glorious and great history and heritage that has shaped the modern civilization in the West, including culture, education, and scientific developments. Unlike other religions such as Christianity where science and religion form two separate entities, the study of science has always been compatible with Islam religion. One such contribution is found in the field of mathematics where Muhammad bin Moosaa Al-Khawaarizmi is credited as one of remarkable founders of Algebra. He introduced the basic algebraic methods of balancing and reduction, and developed a number of formulas for solving such problems. In such a way, he Continue reading...

- Problem Statement – Area(s) of Improvement
In any educational process the only way for a student to learn is by actually remembering what they have been taught. This is doubly true in any of the more precise subject such as math, science and technology; all of which rely on solid evidence to prove someone’s point and more importantly, numbers. By this very attribute, math has gained the ire of students around the world despite the numerous improvements and possibilities the field has provided to society.
In this light, the main problem that this research paper is trying to Continue reading...

Thesis Statement

Algebra is one of the broadest terms used in the field of mathematics with its application in real life situations traceable way back in the ancient Babylonian times over four thousand years ago. The development of algebra was based on finding a solution to solving arithmetic equations mostly in the religious rituals and dilemmas. Most of the renown historical mathematicians such Rene Descartes made some of the major contributions to the development of the modern algebra whereby he came up with la geometre, a publication which focused on improving problem solving techniques in the field of geometry. However, the Continue reading...

Introduction

The Hindu-Arabic numerals are said to have come from the Hindus, Egyptians, Persians and Arabs. There is a presumption that the interrelation between traders served in carrying the symbols from one region to another and hence the accumulation from the different origins. Nonetheless, India is said to be the country that first used the largest number of numerals. The numeral system was established in ancient India. Prior to the emergence of Arab Empire the numeral system of the Hindu and Arabs was already going towards the West. The Arabs adopted the nine numerals in the 9th century. Initially, it Continue reading...

Mathematics is a creative and reasoning activity engaging generalization and abstraction to recognize, define and use relationships and pattern. Math’s symbolic nature gives a powerful, concise and precise means of communication. Mathematical concepts have progressed across all humanities from ancient times and are always advancing. It is essential to technological and scientific development in many arenas of endeavor. Moreover, to its applied usage, learning mathematics is a valuable quest in its own right, giving opportunities for challenge, originality, and leisure (Board of Studies NSW, 2012). To learn mathematics, students must be taught with a curriculum or syllabus that Continue reading...

The scientific revolution of the 17th century is strongly associated with the name of a genius scholar Isaak Newton. His contribution to the world’s scientific thought can hardly be overestimated.
Born in 1642 on the Christmas night in Woolsthhorpe, which is situated in Lincolnshire, England, the child was destined to change the world and become the culminating figure in the revolution of scientific knowledge. A genius as he was, Isaak Newton left his legacy in every fundamental area of that time science: mathematics, mechanics, optics and astronomy.
Isaak stepped into this world in the farmer’s family but Continue reading...

According to Stanoyevitch (2010), cryptography refers to one of the oldest branches of pure mathematics that primarily deal with the study of integers. It deals with the prime numbers and also the properties of the objects which are made out of the integers like the algebraic integers. Cryptography is a very important tool for protecting information from unauthorized access in the computer systems. Currently, finite fields are becoming very vital in cryptography. Most cryptographic algorithms depend heavily on the properties of the finite fields especially the elliptic curve cryptography and the Advanced Encryption Standard (AES). The most important concepts Continue reading...

Muhammad ben Musa al-Khwarizmi

Muhammad ben Musa al-Khwarizmi was a Persian astrophysicist, geometrician, and geographer. He was born in Persia at around 780 and died around 850. Though his name signifies that his family was originally from the region around Khwarizmi nearby the Aral Sea, historians trust that al-Khwarizmi was congenital in the town of Baghdad, which the current day Iraq. Though diminutive is identified about his cloistered life, al-Khwarizmi’s effort and participation have principally endured the ages discreetly intact. The exclusion is a volume of mathematics in which the novel cannot be established; there is, though, a Latin rendition of his Continue reading...

Introduction

Pythagoras theorem is named after a Greek mathematician Pythagoras who lived in 475BC. Despite the theorem being named after him, he was not the only ancient person who came up or probably used the theorem because the Babylonians and used it in ancient civilization. In the theorem Pythagoras creates a relationship between the hypotenuse and two sides of a right angled triangle as a2 + b2 = c2. Later on, mathematician from north Europe came up with Pythagoras triples to simplify on ways of obtaining sides of right angled triangles. As years went by, different mathematicians came up with different was Continue reading...

Personal Portfolio

During my studies at the university I have taken courses in algebra, statistics, English, history, wind energy, and pharmacology. This wide variety of courses has helped prepare me for interdisciplinary studies in that I am creating a wide base and background of basic knowledge in multiple areas. This variety will give me a basis well in the range of areas as they move into upper-level courses and become more specialized in certain areas during my studies in my later years of schooling.
The algebra course that I took builds on basic knowledge that is required of high school graduates. Continue reading...